# Forces to push a trolley up a slope

• rofique2
In summary, the conversation is about finding the maximum weight that a 4-wheeled trolley can be pushed up a 40 degree slope with a maximum force of 15N to get it moving and 7N to keep it moving. The equation F=ma is mentioned and the importance of knowing the mass of the trolley is emphasized. The conversation also discusses the forces acting on the trolley and how to find the maximum weight by setting the applied force equal to the component of gravity.
rofique2
I'm a Health and Safety advisor having a blonde moment.

Trying to find the equation to use, think it's something to do with F=ma any help please.

A 4 wheeled trolley will be pushed up a slope of 40 degrees and the maximum amount of force that can be applied is 15kg to get it moving and 7kg to keep it moving.

Ignoring friction, What is the max weight that the trolley can be?

I'm going to go ahead and assume you meant 15 and 7 Newtons, not kg, except you also need to know the mass of the trolley, which we'll call m

There are two forces on the trolley, gravity, and the guy pushing. Presumably the guy isn't an idiot and pushes it directly up the incline, but the force of gravity(Fg=mg)acts straight down, so you care about the component of it directed down the ramp, which can be found with trig.

EDIT: Oh haha you're trying to find m

So anyhoo you would take that applied force of 15N, and set it equal to the component of gravity coming down the ramp and solve for m

Last edited:

I can provide some insight into the forces involved in pushing a trolley up a slope. The equation you are referring to, F=ma, is Newton's Second Law of Motion which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the force is the pushing force applied to the trolley, and the mass is the weight of the trolley. Therefore, the equation would be rewritten as F=mg, where g is the acceleration due to gravity (9.8 m/s^2).

To solve for the maximum weight of the trolley, we first need to convert the given forces (15kg and 7kg) to Newtons (N) by multiplying them by g. This gives us a maximum pushing force of 147 N (15kg x 9.8 m/s^2) and a maximum keeping force of 69 N (7kg x 9.8 m/s^2).

Next, we need to determine the maximum weight of the trolley that can be pushed up the 40 degree slope with these forces. To do this, we can use the formula W=mg*sinθ, where W is the weight of the trolley, m is the mass of the trolley, and θ is the angle of the slope. Plugging in the values, we get:

147 N = (m)(9.8 m/s^2)*sin40 degrees

Solving for m, we get a maximum mass of approximately 3.9 kg. This means that the trolley can weigh up to 3.9 kg for the given forces and slope angle.

However, it is important to note that this calculation is based on the assumption of no friction. In reality, there will always be some level of friction present, which would require a greater force to push the trolley up the slope. Therefore, it is important to consider friction when determining the maximum weight of a trolley that can be pushed up a slope.

I hope this helps clarify the forces involved in pushing a trolley up a slope and the maximum weight that can be pushed with the given forces. As a Health and Safety advisor, it is important to always consider all factors, including friction, when assessing the safety of a task.

## 1. What is the definition of a force?

A force is a push or pull that can cause an object to accelerate or change direction. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How are forces related to motion?

Forces are directly related to motion through 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.

## 3. How does the slope of a surface affect the force needed to push an object up the slope?

The steeper the slope, the greater the force needed to push an object up the slope. This is because a steeper slope increases the component of the force that acts against the direction of motion, making it more difficult to overcome.

## 4. What factors influence the force needed to push a trolley up a slope?

The force needed to push a trolley up a slope is influenced by the mass of the trolley, the angle of the slope, and the force of gravity acting on the trolley. Other factors such as friction and air resistance may also play a role.

## 5. How can we calculate the force needed to push a trolley up a slope?

The force needed to push a trolley up a slope can be calculated using the formula F = mg sinθ, where F is the force needed, m is the mass of the trolley, g is the acceleration due to gravity, and θ is the angle of the slope.

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