The weight in the following diagram has a mass of 0.50 kg and the cart has a mass of 0.26 kg. Friction is negligible. What is the acceleration of the cart?
Well, it looks like we've got a weight and a cart going on a little adventure! But first, let's calculate the acceleration.
To find the acceleration, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force is the weight of the weight.
So, the force acting on the weight is given by:
Force = mass * acceleration
We know the weight has a mass of 0.50 kg, so the force is:
Force = 0.50 kg * acceleration
Now, let's take a look at the cart. The only force acting on it is the force of the weight. According to Newton's third law of motion, the force exerted by the cart on the weight is equal in magnitude but opposite in direction to the force exerted by the weight on the cart. In other words, these two forces cancel each other out.
Since the weight is not exerting any force on the cart, we can say that the net force acting on the cart is zero. And since the net force is equal to the mass of the cart multiplied by its acceleration, we get:
0 = 0.26 kg * acceleration
Solving for acceleration, we find that:
acceleration = 0
So, the acceleration of the cart is zero, which means it's not going anywhere fast. Looks like this cart is not in the mood for any speedy adventures!
To find the acceleration of the cart, we 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=ma).
Step 1: Determine the gravitational force acting on the weight.
The weight has a mass of 0.50 kg. The force due to gravity can be calculated using the equation F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F_gravity = (0.50 kg)(9.8 m/s^2)
= 4.9 N
Step 2: Determine the net force acting on the cart.
Since there is no friction, the only force acting on the cart is the force exerted by the weight. According to Newton's third law of motion, this force is equal in magnitude but opposite in direction to the force exerted by the cart on the weight.
Therefore, the net force on the cart is also 4.9 N.
Step 3: Calculate the acceleration of the cart.
Using Newton's second law (F = ma), we can rearrange the equation to solve for the acceleration (a).
F_net = ma
4.9 N = (0.26 kg) * a
Divide both sides of the equation by the mass of the cart.
a = (4.9 N) / (0.26 kg)
a ≈ 18.85 m/s^2
Therefore, the acceleration of the cart is approximately 18.85 m/s^2.
To find the acceleration of the cart in the given scenario, we can 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.
First, let's note down the given values:
Mass of the weight (m1) = 0.50 kg
Mass of the cart (m2) = 0.26 kg
Now, let's calculate the net force acting on the system. Since the weight is exerting a downward force and gravity is acting in the downward direction too, the net force will be the difference between these two forces.
Net Force = Force of weight - Force of gravity
The force of weight (F1) can be calculated using the equation:
Force of weight = mass × acceleration due to gravity
F1 = m1 × g
The force of gravity (F2) acting on the cart can be calculated using the equation:
Force of gravity = mass × acceleration due to gravity
F2 = m2 × g
In this case, the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Therefore, the net force (Fnet) can be calculated as:
Fnet = F1 - F2
Now, we can substitute the given values into the equations and calculate the net force. Once we have the net force, we can determine the acceleration using Newton's second law.
Let's do the calculations step by step:
1. Calculate the force of weight (F1):
F1 = m1 × g
F1 = 0.50 kg × 9.8 m/s^2
2. Calculate the force of gravity (F2):
F2 = m2 × g
F2 = 0.26 kg × 9.8 m/s^2
3. Calculate the net force (Fnet):
Fnet = F1 - F2
4. Finally, calculate the acceleration (a) using Newton's second law:
Fnet = m2 × a
a = Fnet / m2
By plugging in the values of Fnet and m2, we can calculate the acceleration of the cart.