Question

Use equations (1) and (2) to eliminate T and show that the expression for f is given by f= g (m- M sin theta) - ( m + M) a (1) T- Mg sin theta- f = Ma (2) mg - T = ma

Answer 1

To eliminate T, we solve equation (2) for T and substitute it into equation (1), which allows us to express f as f = g(m - M sin theta) - (m + M)a.

Step-by-step explanation:

To eliminate T from equations (1) and (2), we need to solve one of the equations for T and then substitute that expression into the other equation. Let's solve equation (2) for T:

mg - T = ma
T = mg - ma ...(3)

Now, substitute equation (3) into equation (1):

T - Mg sin theta - f = Ma
(mg - ma) - Mg sin theta - f = Ma

Group like terms to solve for f:

f = mg - Ma - Mg sin theta
f = g(m - M sin theta) - (m + M)a

This shows how we can eliminate T to find an expression for f based on given equations.