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Chapter 11: Q. 40 (page 289)

A 500 g cart is released from rest 1.00 m from the bottom of a frictionless, 30.0掳 ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. FIGURE P11.40 shows the force during the collision. After the cart bounces, how far does it roll back up the ramp?

Short Answer

Expert verified

The distance where cart rolls back up to the ramp is49.8cm

Step by step solution

01

Step 1. Given information

Mass of cart, m=500g

A plot of force v/s time.

02

Step 2. Evaluating the impulse

Impulse in the given case would be the area under the curve,

Jx=12脳base脳heightJx=12脳200脳26.7脳10-3=2.67N.s

03

Step 3. Calculating the velocities

According to the equation of motion,

vi=2gxisin胃vi=2脳9.8脳1脳sin30vi=3.13m/s

Similarly, the final velocity is,

vf=2gxfsin胃vf=2脳9.8脳xf脳sin30vf=3.13xf

04

Step 4. Substitute and evaluate

As we know that, Jx=鈻�p

Hence,

xf=(2.67-(0.5脳(-3.13))3.13脳0.5)2 xf=49.8cm

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