A 15kg wedding cake is allowed to slide freely down a smooth 30degree inclined. Find the resultant force down the inclined and the acceleration of the object.
Fr=Fg sin 30 degree
=masin 30
=15kg×10m/s^2×Sin 30
=150 Sin 30
=75N
Acceleration
F= ma
a= F/m
=75N /15kg
= 5 m/s ^2
Fc=mg = 15kg * 9.8N/kg = 147N @ 30Deg = weight of cake.
1. Fp = 147sin30 = 73.5N = Force parallel to the plane downward.
2. F = ma.
a = F/m = 73.5 / 15 = 4.9m/s^2
Pls help me with this question
To find the resultant force down the inclined plane and the acceleration of the object, we need to use the principles of force and motion.
First, let's draw a force diagram for the wedding cake sliding down the inclined plane. We have three forces acting on the cake:
1. The force of gravity (weight): This force acts vertically downwards and can be calculated using the formula Fg = mg, where m is the mass (15 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Fg = (15 kg) * (9.8 m/s²) = 147 N (rounded to the nearest whole number)
2. The normal force (Fn): This force acts perpendicular to the inclined plane and balances the component of the weight acting perpendicular to the plane. Since the plane is smooth, there is no frictional force acting.
Fn = mg * cos(theta)
Fn = (15 kg) * (9.8 m/s²) * cos(30°) = 127.5 N (rounded to the nearest whole number)
3. The force down the inclined plane (Fdown): This is the force that causes the cake to accelerate down the incline. It can be calculated using the formula Fdown = mg * sin(theta).
Fdown = (15 kg) * (9.8 m/s²) * sin(30°) = 73.5 N (rounded to the nearest whole number)
The resultant force down the inclined plane is equal to the force down the inclined plane (Fdown) because there is no other component along the inclined plane.
So, the resultant force down the inclined plane is 73.5 N.
To determine the acceleration of the object, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the net force is equal to the resultant force down the inclined plane (Fdown).
Acceleration (a) = Fdown / mass
Acceleration (a) = 73.5 N / 15 kg = 4.9 m/s² (rounded to one decimal place)
Therefore, the resultant force down the inclined plane is 73.5 N, and the acceleration of the wedding cake sliding down the inclined plane is 4.9 m/s².