Question

A cart is kept on a horizontal plane exerts a force of 500 N on the plane. The cart is now pulled along the
plane by applying a force of 100 N)making an angle of 30° with horizontal. Find the force pulling the cart
forward. What force is experienced by plane now?
[86.6 N, 450 N]
​

Answer 1

Answer:forlward force will be 86.6N

force on plane is 450N

Explanation:

Answer 2

The value of force pulling the cart and force experienced by the plane is 50√3N and 450N respectively.

Given:-

Force on plane by the cart = 500N (downwards)

Forward force = 100N

Angle with horizontal = 30°

To Find:-

The value of force pulling the cart and force experienced by the plane.

Solution:-

We can easily calculate the value of force pulling the cart and force experienced by the plane by using these simple steps.

As

Force on plane by the cart = 500N (downwards)

Forward force (F) = 100N

Angle with horizontal = 30°

Since, the forward force is acting on an angle with the horizontal, first we need to take its horizon and vertical components.

Horizontal component (Fh) = F cos30

Vertical component (Fv) = F sin30

$Fh =F \cos(30)$

$Fh = F \times \frac{ \sqrt{3} }{2}$

$Fh = 100 \times \frac{ \sqrt{3} }{2}$

$Fh = 50 \sqrt{3}$

$Fv = F \sin(30)$

$Fv = F \times \frac{1}{2}$

$Fv = 100 \times \frac{1}{2}$

$Fv = 50$

Here, 50√3N force is required for pulling the cart.

And,

Force experienced by the plane = 500 - 50 = 450N

Hence, The value of force pulling the cart and force experienced by the plane is 50√3N and 450N respectively.

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