calculating acceleration from force and mass

acceleration force and mass

A change in an objects motionsuch as Xander speeding up on his scooteris called acceleration. Acceleration occurs whenever an object is acted upon by an unbalanced force. The greater the net force acting on the object, the greater its acceleration will be, but the mass of the object also affects its acceleration. The smaller its mass is, the greater its acceleration for a given amount of force. Newtons second law of motion summarizes these relationships. According to this law, the acceleration of an object equals the net force acting on it divided by its mass. This can be represented by the equation: Acceleration = Net force Mass or a = F m

calculating acceleration

This equation for acceleration can be used to calculate the acceleration of an object that is acted on by a net force. For example, Xander and his scooter have a total mass of 50 kilograms. Assume that the net force acting on Xander and the scooter is 25 Newtons. What is his acceleration? Substitute the relevant values into the equation for acceleration: F = 25 N = 0.5 N a= m 50 kg kg The Newton is the SI unit for force. It is defined as the force needed to cause a 1-kilogram mass to accelerate at 1 m/s2 . Therefore, force can also be expressed in the unit kg m/s2 . This way of expressing force can be substituted for Newtons in Xanders acceleration so the answer is expressed in the SI unit for acceleration, which is m/s2 : 2 0.5 kgm/s a = 0.5kgN = = 0.5 m/s2 kg Q: Why are there no kilograms in the final answer to this problem? A: The kilogram units in the numerator and denominator of the fraction cancel out. As a result, the answer is expressed in the correct SI units for acceleration.

calculating force

Its often easier to measure the mass and acceleration of an object than the net force acting on it. Mass can be measured with a balance, and average acceleration can be calculated from velocity and time. However, net force may be a combination of many unseen forces, such as gravity, friction with surfaces, and air resistance. Therefore, it may be more useful to know how to calculate the net force acting on an object from its mass and acceleration. The equation for acceleration above can be rewritten to solve for net force as: Net Force = Mass Acceleration, or F=ma Look at Xander in the Figure 1.1. Hes riding his scooter down a ramp. Assume that his acceleration is 0.8 m/s2 . How much force does it take for him to accelerate at this rate? Substitute the relevant values into the equation for force to find the answer: F = m a = 50 kg 0.8 m/s2 = 40 kg m/s2 , or 40 N Q: If Xander and his scooter actually had a mass of 40 kg instead of 50 kg, how much force would it take for him to accelerate at 0.8 m/s2 ?

textbook_image

instructional diagrams

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questions

any change in an objects motion is called velocity.

a. true

-->  b. false

the greater the net force acting on an object, the greater its acceleration will be.

-->  a. true

b. false

for a given net force, an object will accelerate less if it has a greater

-->  a) mass.

b) volume.

c) speed.

d) none of the above

one newton is the force needed to cause a

-->  a) 1-kg object to accelerate at 1 m/s2.

b) 1-g object to accelerate at 1 cm/s2.

c) 1-kg object to accelerate at 1 km/s2.

d) none of the above

the si unit for acceleration is

a) cm/s2.

-->  b) m/s2.

c) km/s2.

d) none of the above

diagram questions

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