Block B is initially at rest on the top of cart C. The mass of block B is 10 kg

Question

Block B is initially at rest on the top of cart C. The mass of block B is 10 kg and the coefficient of static friction between B and C is 0.7. The mass of C is 25 kg and the top of the cart makes a 20 degree angle with the horizontal as shown. Force F is then applied to cart C to accelerate the system to the right. Find the maximum possible acceleration of the system for which block B will not slide on cart C.

I know the answer is 2.627 m/s^2 I just need help getting there. Thanks in advance!

Block B is initially at rest on the top of cart C. The mass of block B is 10 kg and the coefficient of static friction between B and C is 0.7. The mass of C is 25 kg and the top of the cart makes a 20 degree angle with the horizontal as shown. Force F is then applied to cart C to accelerate the system to the right. Find the maximum possible acceleration of the system for which block B will not slide on cart C. I know the answer is 2.627 m/s^2 I just need help getting there. Thanks in advance!

Explanation / Answer

N =mgcos20-masin20
and
macos20+mgsin20 =N

hence macos20+mgsin20 =0.7*(mgcos20-masin20)

hence a =2.627

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