Question

A cart is being pulled by ahmed north-ward with a force of magnitude 70 n. hamid is pulling the same cart in the south-west direction with a force of magnitude 50 n. calculate the magnitude and direction of the resulting force on the cart

Answer 1

20n is resultant magnitude and will go towards north west

Answer 2

Answer: R makes an angle of 45º with 70 N  force. That is, R is in North-west direction

Explanation:Here, magnitude of first force, say, A = 70 N.

The magnitude of the second force, say, B = 50 N.

Angle θ between the two forces = 90+45 = 135 degrees.

So, the magnitude of the resultant is

R²= A²+B²+2AB .cosθ

R²= 70²+50²+2×70×50×cos(135)

R²= 7400-7000×sin(45)

R = 49.5 N

The magnitude of R = 49.5 N.

The direction is given by

tan∝ = B sinθ ÷ A+B cosθ = 50×sin(135) ÷ 70+50×cos (135)

         = 50×cos 45 ÷ 70-50 sin 45

         = 1.00

∴ ∝ = 45° Thus R makes an angle of 45º with 70 N

force. That is, R is in North-west direction.

(Refer the diagram for more understanding {from textbook} )