Question

question 17
the work you do when pushing a shopping cart twice as far while applying twice the force is
half as much.
twice as much.
four times as much.
the same amount.
question 18
relative to an initial height, an object raised twice as high has a gravitational potential energy
half as much
four times as much.
twice as much.
need more information

Explanation:

Step1: Recall work - formula

The work formula is $W = Fd$, where $W$ is work, $F$ is force and $d$ is distance.

Step2: Calculate new work

Let the initial force be $F_1$ and distance be $d_1$, so initial work $W_1=F_1d_1$. The new force $F_2 = 2F_1$ and new distance $d_2=2d_1$. Then new work $W_2=F_2d_2=(2F_1)\times(2d_1) = 4F_1d_1=4W_1$.

Step3: Recall gravitational - potential - energy formula

The gravitational - potential - energy formula is $U = mgh$, where $U$ is gravitational potential energy, $m$ is mass, $g$ is gravitational acceleration and $h$ is height.

Step4: Calculate new gravitational potential energy

Let the initial height be $h_1$, so initial potential energy $U_1=mgh_1$. The new height $h_2 = 2h_1$, then new potential energy $U_2=mg(2h_1)=2mgh_1 = 2U_1$.

Answer:

Question 17: four times as much.
Question 18: twice as much.