The goliath beetle, can reach a mass of 0.080 kg. Suppose a goliath beetle is placed on a slope that makes an angle of 37.0 degrees with the horizontal. Find the acceleration of the beetle along the slope, assuming the slope is frictionless.

If a force of 1.40 N upward along the slope is applied to the beetle in the problem above, what is the beetle's acceleration?

Use F = ma for the acceleration. In this case, F is component of the weight down the slope. The mass will cancel out.

For part 2 , use F = ma again, but the net force in this case is 1.40 N MINUS the weight component down the slope

for first part F=gravitysin[37] which is 5.9m/s^2

To find the acceleration of the beetle along the slope, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. Mathematically, it can be written as:

a = Fnet / m

In this case, the net force acting on the beetle along the slope is the force applied upward along the slope, which is 1.40 N. The mass of the beetle is given as 0.080 kg.

So, substituting the values into the formula, we get:

a = 1.40 N / 0.080 kg
= 17.5 m/s^2

Therefore, the acceleration of the beetle along the slope, assuming the slope is frictionless, is 17.5 m/s^2.

Let's now move on to the second part of the question.

If a force of 1.40 N upward along the slope is applied to the beetle, it means that there is an external force acting on the beetle in the opposite direction to its acceleration due to gravity. This force opposes the gravitational force, making the net force acting on the beetle to be lower than its weight.

To find the net force, we need to consider the force of gravity acting on the beetle. The weight of an object can be calculated using the formula:

Weight = mass * gravity

In this case, the mass of the beetle is still 0.080 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.

So, the weight of the beetle is:

Weight = 0.080 kg * 9.8 m/s^2
= 0.784 N

Since the force applied upward along the slope is 1.40 N and opposes the force of gravity, the net force acting on the beetle is:

Net force = applied force - weight
= 1.40 N - 0.784 N
= 0.616 N

Now, we can calculate the acceleration of the beetle using Newton's second law, as we did earlier:

a = Fnet / m
= 0.616 N / 0.080 kg
= 7.70 m/s^2

Therefore, the beetle's acceleration, when a force of 1.40 N upward along the slope is applied, is 7.70 m/s^2.