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Chapter 6: Q. 48 (page 156)

An object of mass m is at rest at the top of a smooth slope of height hand lengthL. The coefficient of kinetic friction between the object and the surface, μk, is small enough that the object will slide down the slope after being given a very small push to get it started. Find an expression for the object’s speed at the bottom of the slope.

Short Answer

Expert verified

The velocity of an object down the slope isvf=2L(μkg-gsinθ)

Step by step solution

01

Step 1. Given Information

A smooth slope of height hand length L

The coefficient of kinetic friction isμk

02

Step 2. Find the speed of object

We need to determine the speed of an object at the bottom of the slope, it was at rest the top and started from here

From the diagram below,

Using Newton's second law, resolving all forces acting along xaxis, we get

F→net=f→k-F→Gsinθ

where θ=tan-1hL;fk⇀=μkmg;FG⇀=mg;F⇀net=ma

⇒ma=μkmg-mgsinθa=μkg-gsinθ

with this acceleration, the object will slide downwards hence to find speed we use the equation of motion,

vf2=vi2+2asvf2=02+2(μkg-gsinθ)×Lvf=2L(μkg-gsinθ)

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Most popular questions from this chapter

A football coach sits on a sled while two of his players build their strength by dragging the sled across the field with ropes. The friction force on the sled is 1000N, the players have equal pulls, and the angle between the two ropes is 20°. How hard must each player pull to drag the coach at a steady2.0m/s?

An object with cross section A is shot horizontally across frictionless ice. Its initial velocity is v0xat t0=0s. Air resistance is not negligible.

a. Show that the velocity at time t is given by the expression

vx=v0x1+CρAv0xt/2m

b. A 1.6-m-wide, 1.4-m-high, 1500kgcar with a drag coefficient of 0.35hits a very slick patch of ice while going 20m/s. If friction is neglected, how long will it take until the car’s speed drops to 10m/s? To 5m/s?

c. Assess whether or not it is reasonable to neglect kinetic friction.

A 4000kg truck is parked on a 15°slope. How big is the friction force on the truck? The coefficient of static friction between the tires and the road is 0.90.

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c. After the elevator reaches its cruising speed?

A block pushed along the floor with velocity v0xslides a distance d after the pushing force is removed.

a. If the mass of the block is doubled but its initial velocity is not changed, what distance does the block slide before stopping?

b. If the initial velocity is doubled to2v0x but the mass is not changed, what distance does the block slide before stopping?
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