Suppose someone is pulling a cart up a ramp. At first they pull the cart paralle

Question

Suppose someone is pulling a cart up a ramp. At first they pull the cart parallel to the ramp, which has an angle of 20 degrees. Now, if the person then decides to pull the cart up the ramp (which has an angle of 20 degrees) not along the line of motion but instead at a 45 degree angle. What will be the applied force measured by a probe? Smaller, larger, the same?

Is it

1)The larger the angle between the pull direction and the ramp the smaller force

2)The higher up the ramp you pull the, the larger the force    

3)The lower down the ramp the cart is the smaller force.

4)The force is larger if the angle between the pull direction and the ramp is positive (string point upwards) and smaller if the angle is negative (string points downwards)

5)) The larger the angle between the pull direction and the ramp the larger the force. Same force regardless of the angle between the pull direction and the ramp

Explanation / Answer

assuming a frictionless surface.
if force of pulling is F and it makes an angle of theta with horizontal,

then its component along the ramp will have to balance the component of weight of the cart.

let the weight of the cart be W.

then F*cos(20-theta)=W*sin(20)

hence when theta=0,
F=0.364*W

when theta=45,

F=0.3774*W

hence when angle is 45 degrees, the force measured will be higher.

hence option 5 is correct.
The larger the angle between the pull direction and the ramp the larger the force.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.