A mass is measured as 15.0 kg with an uncertainty of ±0.3 kg. If this mass is us
Practice Questions
Q1
A mass is measured as 15.0 kg with an uncertainty of ±0.3 kg. If this mass is used to calculate the force (F = ma) with an acceleration of 9.8 m/s², what is the uncertainty in the force?
0.3 N
2.94 N
0.5 N
1.5 N
Questions & Step-by-Step Solutions
A mass is measured as 15.0 kg with an uncertainty of ±0.3 kg. If this mass is used to calculate the force (F = ma) with an acceleration of 9.8 m/s², what is the uncertainty in the force?
Step 1: Identify the mass and its uncertainty. The mass is 15.0 kg and the uncertainty is ±0.3 kg.
Step 2: Identify the acceleration. The acceleration is 9.8 m/s².
Step 3: Use the formula for force, which is F = ma. Here, 'm' is the mass and 'a' is the acceleration.
Step 4: To find the uncertainty in the force, we need to multiply the acceleration by the uncertainty in the mass.
Step 5: Calculate the uncertainty in the force: Uncertainty in force = acceleration * uncertainty in mass = 9.8 m/s² * 0.3 kg.
Step 6: Perform the multiplication: 9.8 * 0.3 = 2.94 N.
Step 7: The uncertainty in the force is 2.94 N.
Uncertainty Propagation – Understanding how uncertainties in measurements affect calculated results, particularly in the context of multiplication.
Newton's Second Law – Applying the formula F = ma to calculate force based on mass and acceleration.
