A 17.0 kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220N and breaks as the elevator accelerates. What was the elevator's minimum acceleration (magnintude and direction)?

Please show me how to do this in addition to the answer. I'm having a lot of trouble in my honors Physics class and any additional tips for these types of problems in general would be greatly appreciated.

The weight of the monkey is
W = M g = 17.0 kg * 9.8 m/s^2 = 166.6 N

If it requires a tension of T = 220 N to break the cord, and if that tension were provided, the monkey would be accelerating upward at a rate "a" given by
T - W = M a
T = W + M a = M (a + g)= 220 N
(a + g) = T/M = 12.9 m/s^2
a = 12.9 - 9.8 m/s^2 = 3.1 m/s^2

Monkey= Mass x g= 17 x 9.8 = 166.6

T= 220
T-W=MA
220 - 166.6=MA
A=220 - 166.6/17
A=3.15

3.14 m/s^2

To solve this problem, we will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the tension in the cord.

First, calculate the weight of the monkey using the formula W = m * g, where m is the mass of the monkey (17.0 kg) and g is the acceleration due to gravity (9.8 m/s^2).
W = 17.0 kg * 9.8 m/s^2 = 166.6 N

Next, set up an equation for the net force acting on the monkey. The tension in the cord (T) is the upward force acting on the monkey, and the weight (W) is the downward force acting on the monkey. Since the cord breaks, the tension is equal to the weight plus the mass of the monkey multiplied by the acceleration (T = W + m * a).
T = W + m * a

Substitute the values we know: T = 220 N, W = 166.6 N, and m = 17.0 kg.
220 N = 166.6 N + 17.0 kg * a

Simplify the equation:
220 N = 166.6 N + 17.0 kg * a
53.4 N = 17.0 kg * a

Solve for the acceleration:
a = 53.4 N / 17.0 kg
a ≈ 3.14 m/s^2

Therefore, the elevator's minimum acceleration is approximately 3.14 m/s^2, in the upward direction.

In general for these types of problems, it's important to:
1. Identify the forces acting on the object (e.g., tension, weight).
2. Set up an equation using Newton's second law (net force = mass * acceleration).
3. Substitute the given values and solve for the unknown variable.

To solve this problem, you need to apply Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a). In this case, the monkey hanging from the cord is experiencing two forces: its weight (downward) and the tension in the cord (upward).

First, calculate the weight of the monkey using the formula W = M * g, where M is the mass of the monkey and g is the acceleration due to gravity (approximately 9.8 m/s²). In this case, M = 17.0 kg, so W = 17.0 kg * 9.8 m/s² = 166.6 N.

Next, set up an equation to find the minimum acceleration of the elevator (a) using the tension force (T) and the weight (W) of the monkey. We know that T = W + M * a, where T is the tension in the cord. Rearrange this equation to solve for a: a = (T - W) / M.

Given that the tension in the cord is T = 220 N, substitute the values into the equation: a = (220 N - 166.6 N) / 17.0 kg ≈ 3.1 m/s².

Therefore, the minimum acceleration of the elevator, in magnitude and direction, is approximately 3.1 m/s² upward.