Question 1

A system of blocks and a frictionless pulley is shown in the figure.Block A has a mass of 2.0 kg and is on a rough horizontal surface for which μ_s = 0.40 between the surface and block A.The rope pulls horizontally on block A.Block C has a mass of 1.0 kg.An external force ,applied vertically to block A,maintains the system at rest as shown in the figure.What is the friction force on block A?

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Question 2

A 1520-N crate is to be held in place on a ramp that rises at 30.0° above the horizontal (see figure).The massless rope attached to the crate makes a 22.0° angle above the surface of the ramp.The coefficients of friction between the crate and the surface of the ramp are  and  .The pulley has no appreciable mass or friction.What is the MAXIMUM weight w that can be used to hold this crate stationary on the ramp?

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Question 3

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600.What is the maximum speed at which the car can travel around this curve without sliding?

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Question 4

The figure shows a 2000 kg cable car descending a high hill.A counterweight of mass  on the other side of the hill aids the brakes in controlling the cable car's speed.The rolling friction of both the cable car and the counterweight are negligible.How much braking force does the cable car need to descend at constant speed?

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Question 5

Engineers are designing a curved section of a highway.If the radius of curvature of the curve is  at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

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Question 6

Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure).P is closest to

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Question 7

Block A of mass 8.0 kg and block X are attached to a rope that passes over a pulley.A 50-N force P is applied horizontally to block A,keeping it in contact with a rough vertical face.The coefficients of static and kinetic friction between the wall and block A are  and  .The pulley is light and frictionless.In the figure,the mass of block X is adjusted until block A descends at constant velocity of 4.75 cm/s when it is set into motion.What is the mass of block X?

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Question 8

In the figure,a block of mass M hangs at rest.The rope that is fastened to the wall is horizontal and has a tension off 52 N.The rope that is fastened to the ceiling has a tension of  and makes an angle θ with the ceiling.What is the angle θ?

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Question 9

A 600-kg car traveling at  is going around a curve having a radius of 120 m that is banked at an angle of 20°.
(a)Is the curve properly banked for the car's speed?
(b)What is the minimum coefficient of static friction required between the road and the car's tires so the car does not skid?

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Question 10

A 23 kg mass is connected to a nail on a frictionless table by a massless string 1.3 m long.There is no appreciable friction between the nail and the string.If the tension in the string is  while the mass moves in a uniform circle on the table,how long does it take for the mass to make one complete revolution?

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Question 11

The figure shows two forces,each of magnitude 4.6 N,acting on an object.The angle between these forces is 40°,and they make equal angles above and below the horizontal.What third force will cause the object to be in equilibrium (acceleration equals zero)?

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Question 12

Two blocks are connected by a string that goes over an ideal pulley as shown in the figure and pulls on block A parallel to the surface of the plane.Block A has a mass of 3.00 kg and can slide along a rough plane inclined 30.0° to the horizontal.The coefficient of static friction between block A and the plane is 0.400.What mass should block B have in order to start block A sliding up the plane?

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Question 13

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m.What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?

Accepted Answer

The minimum coefficient of static friction ($μ_s$) required to prevent the car from sliding can be found using the formula for centripetal force ($F_c$) required to keep an object moving in a circle of radius $r$ at a constant speed $v$, which is $F_c = \frac{mv^2}{r}$, where $m$ is the mass of the object. The frictional force ($F_f$) that provides this centripetal force is given by $F_f = μ_sN$, where $N$ is the normal force. In this case, since the car is on a horizontal surface, $N = mg$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Setting $F_c = F_f$, we get $\frac{mv^2}{r} = μ_smg$. The mass ($m$) cancels out, and solving for $μ_s$ gives $μ_s = \frac{v^2}{rg}$. Substituting the given values ($v = 40.0 m/s$, $r = 200 m$, and $g = 9.8 m/s^2$) into the equation yields $μ_s = \frac{(40.0)^2}{200 \times 9.8} = \frac{1600}{1960} = 0.816$, which matches choice B.

Question 14

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of  .What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

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Question 15

A traffic light weighing 100 N is supported by two ropes as shown in the figure.The tensions in the ropes are closest to

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Question 16

A 600-kg car traveling at  is going around a curve having a radius of 120 m that is banked at an angle of 25.0°.The coefficient of static friction between the car's tires and the road is 0.300.What is the magnitude of the force exerted by friction on the car?

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The answer of A 600-kg car traveling at  is...

Question 17

A 250-kg crate is on a rough ramp,inclined at 30° above the horizontal.The coefficient of kinetic friction between the crate and ramp is 0.22.A horizontal force of 5000 N is applied to the crate,pushing it up the ramp.What is the acceleration of the crate?

Accepted Answer

The force of friction is:$$f_k=\mu_k n=\mu_k mg\cos	heta$$The net force on the crate is:$$F_{net}=F-f_k=ma$$$$a=\frac{F-\mu_k mg\cos	heta}{m}$$$$a=\frac{5000	ext{ N}-(0.22)(250	ext{ kg})(9.8	ext{ m/s}^2)\cos30\degree}{250	ext{ kg}}$$$$a=8.4	ext{ m/s}^2$$

Question 18

The figure shows two forces acting at right angles on an object.They have magnitudes  and  .What third force will cause the object to be in equilibrium (acceleration equals zero)?

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Question 19

A car drives over a hilltop that has a radius of curvature 0.120 km at the top of the hill.At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

Accepted Answer

For the tires to just barely lose contact with the road at the top of the hill, the centripetal force must equal the gravitational force acting on the car. The formula for centripetal force is $F_c = \frac{mv^2}{r}$, where $m$ is the mass of the car, $v$ is the velocity, and $r$ is the radius of curvature. The gravitational force is $F_g = mg$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Setting these two forces equal gives $\frac{mv^2}{r} = mg$, which simplifies to $v^2 = rg$. Plugging in $r = 0.120 km = 120 m$ and $g = 9.8 m/s^2$, we find $v = \sqrt{120m \times 9.8 m/s^2} = \sqrt{1176} m/s \approx 34.3 m/s$.

Question 20

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m.The coefficient of static friction between the tires and the road is 0.350.At what speed will the car begin to skid sideways?

Accepted Answer

The car will begin to skid sideways when the centripetal force required to keep the car moving in a circle exceeds the maximum static friction force. The maximum static friction force can be calculated using $f_{\text{max}} = \mu_s N$, where $\mu_s$ is the coefficient of static friction and $N$ is the normal force. For a car of mass $m$ on a horizontal surface, $N = mg$, where $g$ is the acceleration due to gravity ($9.8 \, \text{m/s}^2$). The centripetal force required for circular motion is given by $F_c = \frac{mv^2}{r}$, where $v$ is the velocity of the car and $r$ is the radius of the curve. Setting the maximum static friction force equal to the required centripetal force gives $\mu_s mg = \frac{mv^2}{r}$. Solving for $v$ gives $v = \sqrt{\mu_s g r}$. Substituting $\mu_s = 0.350$, $g = 9.8 \, \text{m/s}^2$, and $r = 100 \, \text{m}$ gives $v = \sqrt{0.350 \times 9.8 \times 100} = \sqrt{343} \approx 18.5 \, \text{m/s}$.

Quiz 5: Applying Newtons Laws

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600.What is the maximum speed at which the car can travel around this curve without sliding?

Engineers are designing a curved section of a highway.If the radius of curvature of the curve is at what angle should the curve be banked so that a car traveling at 29.0 m/s will stay on the road without the aid of frictional forces?

Two weights are connected by a massless wire and pulled upward with a constant speed of 1.50 m/s by a vertical pull P.The tension in the wire is T (see figure) .P is closest to

In the figure,a block of mass M hangs at rest.The rope that is fastened to the wall is horizontal and has a tension off 52 N.The rope that is fastened to the ceiling has a tension of and makes an angle θ with the ceiling.What is the angle θ?

A 600-kg car traveling at is going around a curve having a radius of 120 m that is banked at an angle of 20°. (a)Is the curve properly banked for the car's speed? (b)What is the minimum coefficient of static friction required between the road and the car's tires so the car does not skid?

The figure shows two forces,each of magnitude 4.6 N,acting on an object.The angle between these forces is 40°,and they make equal angles above and below the horizontal.What third force will cause the object to be in equilibrium (acceleration equals zero) ?

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m.What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?

A 600-kg car is going around a banked curve with a radius of 110 m at a speed of .What is the appropriate banking angle so that the car stays on its path without the assistance of friction?

A traffic light weighing 100 N is supported by two ropes as shown in the figure.The tensions in the ropes are closest to

A 600-kg car traveling at is going around a curve having a radius of 120 m that is banked at an angle of 25.0°.The coefficient of static friction between the car's tires and the road is 0.300.What is the magnitude of the force exerted by friction on the car?

A 250-kg crate is on a rough ramp,inclined at 30° above the horizontal.The coefficient of kinetic friction between the crate and ramp is 0.22.A horizontal force of 5000 N is applied to the crate,pushing it up the ramp.What is the acceleration of the crate?

The figure shows two forces acting at right angles on an object.They have magnitudes and .What third force will cause the object to be in equilibrium (acceleration equals zero) ?

A car drives over a hilltop that has a radius of curvature 0.120 km at the top of the hill.At what speed would the car be traveling when it tires just barely lose contact with the road when the car is at the top of the hill?

A 1000-kg car is slowly picking up speed as it goes around a horizontal curve whose radius is 100 m.The coefficient of static friction between the tires and the road is 0.350.At what speed will the car begin to skid sideways?