Tom enlists the help of his friend John to move his car. They apply forces to th

Question

Tom enlists the help of his friend John to move his car. They apply forces to the car as shown in the diagram. Here |F_1| = 427 N, |F_2| = 345 N and friction is negligible. Mass of the car = 3.50 x 10^3 kg, theta_1 = 12.0 degree, and theta_2 = 25.0 degree. The diagram below shows the top view of the car which is in the x-z plane (horizontal plane). Find the resultant force exerted on the car. (Express your answer in vector notation.) What is the acceleration of the car? (Express your answer in vector notation.)

Explanation / Answer

here,

F1 = 427 N * ( cos(theta) i + sin(theta1) k)

F1 = 417.7 N i + 88.8 N k

F2 = 345 * ( cos(theta2) i - sin(theta2) k) N

F2 = 312.7 N i - 145.8 N k

the resultant force , F = F1 + F2

F = 730.4 N i - 57 N k

|F| = sqrt(730.4^2 + 57^2)

|F| = 732.6 N

b)

the accelration , a = |F| /m

a = 732.6 /3500

a = 0.21 m/s^2

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