Question

A car weighing 1400 kg is moving at a speed of 54 km/h up a hill when the motor stops. If it is just able to reach the destination which is at a height of 10 m above the point, calculate the work done against friction (negative of the work done by friction).

Answer 1

Dear Student,

◆ Answer -

W = 20300 J

● Explanation -

# Given -

m = 1400 kg

v = 54 km/h = 15 m/s

h = 10 m

# Solution -

Work done against friction is -

W = KE - PE

W = 1/2 mv^2 - mgh

W = 1/2 × 1400 × 15^2 - 1400 × 9.8 × 10

W = 157500 - 137200

W = 20300 J

Hence, work done against friction is 20300 J.

Thanks dear. Hope this helps you..

Answer 2

A car weighing 1400 kg is moving at a speed of 54 km/h up a hill when the motor stops. If it is just able to reach the destination which is at a height of 10 m above the point, then the work done against friction is -20,300

Explanation:

Step 1:

Given values in the question :-

Car Mass m = 1400 kg .

h = 10 m

Initial velocity v= 54 km / h = (54000/3600) m / s = 15 m / sec.

Step 2:

Now the car's first kinetic energy  $=\frac{1}{2} m v^{2}$

$\begin{aligned}&=\frac{1}{2} \times 1400 \times 15^{2}\\&=\frac{1}{2} \times 1400 \times 225\\&=\frac{1}{2} \times 315000\\&=157500 \mathrm{J}\end{aligned}$

Here the final speed and the final kinetic energy are both Zero = Final - Initial

$\begin{aligned}&=0-157500\\&=-157500 \mathrm{J}\end{aligned}$

Step 3:

Thus the increase in kinetic energy is by all force equal to W.D.

That's how gravity works,= mgh

$=1400 \times 9.8(-10)$

$=1400 \times -98$

$=-137200$

Step 4:

Shift in kinetic energy = Work done through friction + Work done through gravity.

$-157500=\text { Work done by friction }+(-137200)$

Therefore Work done by the friction is given by the following

Work done  $=-157500+137200$

= -20,300

Therefore, the friction function is 20300 J