A wooden crate of mass 20kg is pulled in a straight line along a rough horizontal floor using a handle attached to the crate - Edexcel - A-Level Maths Mechanics - Question 7 - 2018 - Paper 2

To find the acceleration of the crate, we start by analyzing the forces acting on it:

1. Identify Forces: The forces include the tension in the handle (T = 40N), the weight of the crate (W = mg = 20kg * 9.81m/s²), and the frictional force (F_friction). The frictional force can be calculated as:

   $F_{friction} = \mu \cdot N$

   where ( \mu = 0.14 ) and ( N = mg - T \sin(\alpha) ).

2. Calculate Normal Force: The normal force (N) can be calculated as: $N = mg - T\sin(\alpha)$ Using that ( \sin(\alpha) = \frac{3}{5} ) and that ( T = 40N ): $N = 20kg * 9.81m/s² - 40N * \frac{3}{5}$ $= 196.2N - 24N = 172.2N.$

3. Calculate Frictional Force: Then, $F_{friction} = 0.14 * 172.2N ≈ 24.072N$

4. Sum of Forces: The net force acting on the crate in the horizontal direction is: $F_{net} = T\cos(\alpha) - F_{friction}$ where ( \cos(\alpha) = \frac{4}{5} ), therefore, $F_{net} = 40N * \frac{4}{5} - 24.072N$ $= 32N - 24.072N ≈ 7.928N$

5. Calculate Acceleration (a): Then, applying Newton's second law, $a = \frac{F_{net}}{m} = \frac{7.928N}{20kg} ≈ 0.3964 m/s²$

Thus, the acceleration of the crate is approximately $0.40 m/s²$.