trevor is pulling his younger brother in a wagon. he pulls the wagon 50 m to the corner with a force that is…
trevor is pulling his younger brother in a wagon. he pulls the wagon 50 m to the corner with a force that is parallel with the ground. he then turns the wagon around and pulls it 50 m back to the starting point with the same force at an angle of 30° with respect to the ground. how does the amount of work trevor performs going to the corner compare with the amount of work he performs coming back? they are the same because he uses the same amount of force. they are the same because he travels the same distance. he does less work coming back because the force moving the wagon is only 50cos30°. he does more work coming back because the force moving the wagon is only 50cos60°.
Answer
Explanation:
Step1: Recall work - formula
The work - formula is $W = F\cdot d\cdot\cos\theta$, where $W$ is work, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and the displacement.
Step2: Calculate work going to the corner
When going to the corner, $\theta_1 = 0^{\circ}$, $d_1=50\ m$. So $W_1 = F\cdot d_1\cdot\cos\theta_1=F\times50\times\cos0^{\circ}=50F$ (since $\cos0^{\circ}=1$).
Step3: Calculate work coming back
When coming back, $\theta_2 = 30^{\circ}$, $d_2 = 50\ m$. So $W_2=F\cdot d_2\cdot\cos\theta_2=F\times50\times\cos30^{\circ}=50F\times\frac{\sqrt{3}}{2}\approx43.3F$. Since $W_2 = 50F\cos30^{\circ}<W_1 = 50F$, he does less work coming back because the force moving the wagon in the direction of displacement is $F\cos30^{\circ}$ (assuming the magnitude of the force is $F$).
Answer:
He does less work coming back because the force moving the wagon is only $F\cos30^{\circ}$ (equivalent to the option "He does less work coming back because the force moving the wagon is only $50\cos30^{\circ}$" if we assume the magnitude of the force is 1 unit for the sake of the ratio - comparison in the options). So the correct option is: He does less work coming back because the force moving the wagon is only $50\cos30^{\circ}$.