A toy car travels around a vertical loop track.
The toy car is released from rest at a height of \(58\,\mathrm{cm}\) above the bottom of the vertical loop.
The car is at a height of \(32\,\mathrm{cm}\) when it is at the top of the vertical loop.
Assume that there are no resistive forces acting on the car.
What is the speed of the car at the top of the vertical loop?
Correct Answer: \( \boxed{\mathrm{B}} \)
By conservation of mechanical energy,
\(mg(0.58)=mg(0.32)+\dfrac{1}{2}mv^2\).
Hence,
\(\dfrac{1}{2}v^2=g(0.26)\).
Using \(g=9.8\,\mathrm{m\,s^{-2}}\),
\(v=\sqrt{2(9.8)(0.26)}\approx2.3\,\mathrm{m\,s^{-1}}\).
Therefore, the correct answer is (B).
The diagram shows a block on a slope.
A constant force of \(1.8\,\mathrm{N}\) in a direction parallel to the slope is exerted on the block. This causes the block to move along the slope at a constant speed.
The block moves a distance of \(8.0\,\mathrm{m}\) along the slope and gains height \(h\). The work done against the frictional force acting on the block is \(4.8\,\mathrm{J}\).
The weight of the block is \(4.0\,\mathrm{N}\).
What is the value of \(h\)?
Correct Answer: \( \boxed{\mathrm{B}} \)
Work done by the applied force is
\(W=Fs=1.8\times8.0=14.4\,\mathrm{J}\).
Since the speed is constant,
\(14.4=4.8+4.0h\).
Hence, \(4.0h=9.6\) and \(h=2.4\,\mathrm{m}\).
Therefore, the correct answer is (B).
Four identical uniform blocks are spread on a table. Each block has mass \(m\) and thickness \(h\).
The acceleration due to free fall is \(g\).
How much work is done on the blocks in stacking them on top of one another?
Correct Answer: \( \boxed{\mathrm{B}} \)
Initially, the centre of mass of each block is at a height of \(\dfrac{h}{2}\).
After stacking, the centres of mass are at
\(\dfrac{h}{2},\ \dfrac{3h}{2},\ \dfrac{5h}{2},\ \dfrac{7h}{2}\).
The increases in height are
\(0,\ h,\ 2h,\ 3h\).
The total increase in gravitational potential energy is
\(mgh(0+1+2+3)=6mgh\).
Therefore, the work done is \(6mgh\).
Therefore, the correct answer is (B).
