Question

A 30-kg shopping cart full of groceries sitting at the top of

Answer 1

Answer:

0.0102 m or 1 cm

Explanation:

Let g = 10m/s2

The potential energy of the shopping cart of the top of the hill is:

$E_p = mgh = 30*9.8*2 = 600 J$

When the cart gets to the bottom of the hill, all this potential energy is converted to kinetic energy:

$E_k = mv^2/2 = 600 J$

$v^2 = \frac{600*2}{30} = 40$

$v = \sqrt{39.2} = 6.324 m/s$

As the cart stop due to the stump, the can of peaches flies with the same speed.

By Newton's 3rd law, the car would exert a 490N force on the can too

The deceleration of the can would then be:

$a = F/m = 490/0.25 = 1960 m/s^2$

This force would stop the can, but not without making a dent, aka a traveled distance on the car skin

We can use the following equation of motion to find out the distance traveled by the can:

$v^2 - v_0^2 = 2a\Delta s$

where v = 0 m/s is the final velocity of the can when it stops, $v_0^2$ = 40m/s is the initial velocity of the can when it hits, a = -1960 m/s2 is the deceleration of the can, and $\Delta s$ is the distance traveled, which we care looking for:

$0 - 40 = 2*(-1960)*\Delta s$

$\Delta s = \frac{40}{2*1960} = 0.0102 m$ or 1 cm